The creamy bleaching agent suspension is mixed with an oxidizing agent prior to applying it to the hair to form a composition for bleaching or decolorizing hair. This creamy bleaching agent suspension contains less than 2.5% by weight water and a mixture of at least one inorganic persalt, at least one alkaline reacting salt, from 0.5 to 20 percent by weight of a thickening substance, which consists essentially of an acrylic acid polymer and one or more cellulose, alginate and/or polysaccharide polymers, and from 26.5 to 35 percent by weight of at least one oil or wax, and, as needed, one or more cosmetic additive ingredient. From 0.1 to 3 percent by weight of the acrylic acid polymer must be present in the composition.